Lattice object / modifier will not bend
To get your Lattice deformation to work:


First of all you have to subdivide a mesh at least with several loopcuts (and the more smooth transitions you want, the more subdivisions you need). To be concrete, exactly this wasn't done for your mesh in the file.
Then add a Lattice Modifier to your mesh, then select created lattice in the "Object" input box of the modifier. 


Only after this is done, will modifications to the Lattice affect the mesh.



EDIT:
Alright, after taking a look a the blendfile, the reason for the modifier's misbehavior became clear: you simply don't have any subdivisions in your mesh, so it cannot bend. The lattice modifier affects existing geometry, and can only move existing vertices. As you can see in the gif below, after I added some subdivisions to the length of your mesh, using the Loop Cut and Slide Tool (CtrlR), the Lattice works fine.